Development of a Cyclic Periodic Wave Function Approach for the Study of Infinitely Periodic Solid-State Systems

Abstract

The ab initio cyclic periodic wave function (CPWF) approach is developed for the treatment of infinitely periodic systems. Using the full infinite Hamiltonian operator, as well as symmetrically identical basis set wave functions that preserve the translational symmetry of the electron density of the system, this approach can be applied at the Hartree–Fock level, or correlation can be directly included by the usual modes. In this approach, all many-body interactions are included, and no edge effects occur. Initial test calculations of the CPWF method at the ab initio Hartree–Fock level are performed on the chains of hydrogen fluoride molecules.

A Cyclic Periodic Wave Function Approach for the Study of Infinitely Periodic Solid-State Systems. I. Application to the C–H···π(C≡C) Hydrogen Bonding Systems

“…The CPWF method has been described in detail in the previous paper, 42 it uses the full infinite Hamiltonian operator for the crystal and begins by assuming an infinite-sized single-Slater determinant form for the ground-state wave function.…”

“…34−38 However, it is still very challenging to study some large molecular systems computationally, such as infinite crystal solids containing weak interactions, by any of the current quantum-mechanical method, since it is necessary to use reasonably large basis sets and high-order correlation corrections simultaneously 39−41 in those large molecular systems. We have developed a new ab initio cyclic periodic wave function (CPWF) method 42 to solve some of the problems involved in these systems. In order for the method to be used to study reasonably large molecular systems in the crystal state, where relatively weak intermolecular interactions may be important, we will apply the method at the AM1 43 and PM3 44,45 semiempirical levels of approximation.…”

A Cyclic Periodic Wave Function Approach for the Study of Infinitely Periodic Solid-State Systems: II. Application to Helical Polysaccharides

“…We will apply the cyclic periodic wave function (CPWF) method, which has been described in detail in the previous paper. 43 This method uses the full infinite Hamiltonian operator with a basis set composed from cyclic periodic wave functions, which use a molecular unit or monomer as the repeat unit rather than using the crystal unit cell. 43 This gives a more chemically intuitive approach since the individual monomer will then provide the 0th-order form.…”

“…43 This method uses the full infinite Hamiltonian operator with a basis set composed from cyclic periodic wave functions, which use a molecular unit or monomer as the repeat unit rather than using the crystal unit cell. 43 This gives a more chemically intuitive approach since the individual monomer will then provide the 0th-order form. The key to this method then rests in the form for the basis set functions, as is shown in eq 1.…”

“…In those large molecular systems, it is computationally demanding to study weak interactions due to the need to simultaneously use relatively large basis sets and high-order correlation corrections. 40−42 We have solved some of these problems successfully by applying the cyclic periodic wave function (CPWF) method 43 at the AM1 44 and PM3 45,46 semiempirical levels of approximation. Our calculation results for the study of infinitely periodic solid-state systems containing very weak CH−pi (C−H•••π) interactions between repeat units are submitted in the previous paper.…”